Here are some graphs of physical processes.

**Can you suggest plausible processes that could have given rise to each graph?**

Now click on the link below to see eight processes that give rise to the graphs.

Can you match each process to a graph?

PROCESSES

- A cup of tea is made and the temperature measured in degrees Celsius every second. What would the temperature - time graph look like?
- The height of the valve on a bicycle tyre above the ground is measured after each centimetre that the bicycle travels forwards. What would the height - distance graph look like?
- I throw a tennis ball straight up into the air and catch it. The height of the ball from the ground is measured over the time of the journey using freeze-frame photography. What would the height - time graph look like?
- I measure several objects using inches and then using metres, plot them on a scatter graph, and join the points. What would the metres - inches graph look like?
- I jump out of a plane and the distance fallen from the plane is measured every $0.1$ second until I open my parachute. What would the distance fallen - time graph look like whilst in freefall?
- I drive at 70 miles an hour along the motorway and note the reading on my odometer (mile counter) every 5 minutes. What would the odometer reading - time graph look like?
- I blow up a roughly spherical balloon using a balloon pump. After each pump I measure the radius of the balloon in centimetres. What would the radius - number of pumps graph look like?
- I suck water through a straw out of a large beaker at a constant rate and measure the volume of liquid remaining at various times. What would the volume-time graph look like?

**Can you suggest equations that could model each of these processes?**

Now click on the link below to see eight equations.

Can you match each equation to the graphs and related processes?

EQUATIONS

$$y=A \sqrt[3]{x}$$ |
$$y = A \sin(Bx)$$ |
$$y = Ax + B$$ |
$$y=\frac{A}{e^x}+B$$ |

$$y=Ax^2$$ |
$$y = Ax^2 + Bx + C$$ |
$$y = Ax$$ |
$$y = Ax+B$$ |

**Extension**

Can you determine values for the constants A, B and C for each equation? For some, you will need to make some assumptions.